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arXiv:2002.10093 · Physical Review A

Generalized framework of weak-value amplification in path interference of polarized light for the enhancement of all possible polarization anisotropy effects

Niladri Modak, B S Athira, Ankit Kumar Singh, Nirmalya Ghosh

Published May 19, 2021• 8 citations
arXivHTMLPDF

Abstract

Using the profound interferometric philosophy of weak-value amplification, we propose a simple, general, and robust polarization method for the amplification and quantification of small magnitudes of all possible polarization anisotropy effects in a single experimental embodiment. The approach is experimentally realized by introducing a weak coupling between the polarization degree of freedom of light and the path degree of freedom in a Mach-Zehnder interferometer in the presence of a weak anisotropy effect. Real and imaginary weak-value amplifications of different polarization anisotropy effects are manifested as characteristic changes in the relevant Stokes vector elements at the exit port of the interferometer, which follow orthogonal trajectories in the Poincar\'e sphere. The proof-of-concept experiment demonstrates that by using this scheme, one can faithfully extract and quantify an anisotropy parameter that is smaller than the typical sensitivity of measurement of a given Stokes parameter of a traditional polarimeter by a large weak-value amplification factor. This opens up the possibility of a sample measuring weak-value polarimeter for studying the rich variety of fundamental optical effects and for materials characterization and precision metrology.

DOI
10.1103/physreva.103.053518

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Using the profound interferometric philosophy of weak-value amplification, we propose a simple, general, and robust polarization method for the amplification and quantification of small magnitudes of all possible polarization anisotropy effects in a single experimental embodiment. The approach is experimentally realized by introducing a weak coupling between the polarization degree of freedom of light and the path degree of freedom in a Mach-Zehnder interferometer in the presence of a weak anisotropy effect. Real and imaginary weak-value amplifications of different polarization anisotropy effects are manifested as characteristic changes in the relevant Stokes vector elements at the exit port of the interferometer, which follow orthogonal trajectories in the Poincar'e sphere. The proof-of-concept experiment demonstrates that by using this scheme, one can faithfully extract and quantify an anisotropy parameter that is smaller than the typical sensitivity of measurement of a given Stokes parameter of a traditional polarimeter by a large weak-value amplification factor. This opens up the possibility of a sample measuring weak-value polarimeter for studying the rich variety of fundamental optical effects and for materials characterization and precision metrology.
Abstract The quantification of simultaneously present weak polarization anisotropy effects are of practical interest from polarimetric and metrological perspective. Recently, in Modak et al (2021 Phys. Rev. A 103 053518), we experimentally demonstrated a classical analog of post-selected quantum weak measurement through optical interferometry to amplify all possible weak polarization anisotropy effects individually. Here, we propose an extension of this interferometric framework for applying it in a realistic scenario to quantify simultaneously present polarization anisotropy effects. Moreover, a clear correspondence of differential Jones matrix approach with the present scheme is indicated. The proposed scheme enables the measurement of differential Jones matrices through characteristic Stokes vector elements. Our proposal leads to a new class of polarimeter for experimental detection of differential Jones matrix of non-depolarizing anisotropic medium exhibiting simultaneous multiple polarimetric effects of tiny magnitude.
The extraordinary concept of weak value amplification and a number of other seemingly counter-intuitive wave phenomena are manifestations of fine interference effects. In this report, we show that weak value amplification naturally arises in the cases of nearly destructive interference between the two orthogonal states of the observable which mimics the corresponding near destructive interference between the eigenstates of the measuring observable as a consequence of nearly mutually orthogonal pre and post selections of the system states. In order to elucidate this, we first experimentally demonstrate a weak measurement concept that uses near destructive interference of two paths of an interferometer having slightly rotated linear polarization states of light. By generating nearly destructive interference between the two paths with small amplitude and phase offsets of the waves, we observe both real and imaginary (respectively) weak value amplification of the small polarization rotation leading to large rotation of the polarization vector orientation and dramatic changes in the circular polarization descriptor fourth Stokes vector element of light, respectively. We go on to demonstrate that the giant enhancement of magneto-optical Kerr rotation, by which we can claim that we have found a non-modulation based and cost-effective magneto-optical Kerr effect (MOKE) measurement. At the end, we show successful weak value amplification of spin Hall shift in magneto-optical sample in both longitudinal and polar MOKE. Our ongoing work is to find out the relation between magneto-optical Kerr rotation and spin Hall shift of light in magnetic material.
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal degree of freedom. We have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.
We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to 400+/-200 frad and the linear travel of a piezo actuator down to 14+/-7 fm.
The extraordinary concept of weak value amplification and a number of other seemingly counter-intuitive wave phenomena are manifestations of fine interference effects. Taking example of one such intriguing wave interference phenomenon, namely, optical Fano resonance, we show that weak value amplification naturally arises in such scenario due to near destructive spectral interference between a continuum mode and a narrow resonance mode which mimics the corresponding near destructive interference between the eigenstates of the measuring observable as a consequence of nearly mutually orthogonal pre and post selections of the system states. In order to elucidate this, we first experimentally demonstrate a weak measurement concept that uses near destructive interference of two paths of an interferometer having slightly rotated linear polarization states of light. By generating nearly destructive interference between the two paths with small amplitude and phase offsets of the waves, we observe both real and imaginary (respectively) weak value amplification of the small polarization rotation leading to large rotation of the polarization vector orientation and dramatic changes in the circular polarization descriptor 4th Stokes vector element of light, respectively. We go on to demonstrate that the giant enhancement of small Faraday rotation in the vicinity of the Fano spectral dip in waveguided magneto-plasmonic crystal is a manifestation of such natural interferometric weak value amplification.
We introduce an ultrasensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA+interferometry uses weak value amplification of the relative delay between two paths to enhance interferometric sensitivity. As an example, we demonstrate a proof-of-principle experiment that achieves few-attosecond timing resolution (few nanometer path length resolution) with a double-slit interferometer using only common optical components. Since our example uses only the spatial shift of double-slit interference fringes, its precision is not limited by the timing resolution of the detectors but is instead limited by the fundamental shot noise associated with classical light and the diminished technical noise. We experimentally demonstrate that the signal-to-noise ratio can be improved by one to two orders of magnitude relative to a measurement that does not use WVA. Two key conclusions are drawn: (i) Most conventional interferometric techniques primarily rely on determining the path difference (time delay or longitudinal phase), with their precision constrained by technical noise. Our protocol offers a robust solution for minimizing the technical noise in traditional interferometry, with precision in principle approaching the shot-noise limit. (ii) Although WVA has achieved significant advancements in ultrasensitive longitudinal phase measurement, its applicability is constrained by the need for broad spectral bandwidths and high-resolution spectrometers. Contrary to previous assumptions, we demonstrate that quantum-limited WVA time delay measurements are achievable with narrow band light using real weak values. Thus, the cost-effectiveness and practicality of the proposed WVA+interferometry protocol using narrow band light broaden the scope of WVA applications. This protocol holds potential for broad applications in optical metrology, quantum optics and quantum information, biomedical imaging, and interferometric telescopes for astrophysics.